Question

Of the following:
(1) $a(x-y)=ax-ay$
(2) $a^{x-y}=a^x-a^y$
(3) $\log (x-y)=\log x-\log y$
(4) $\log x/\log y=\log x-\log y$
(5) $a\left(xy\right)=ax\cdot ay$.

• A. Only $1$ and $4$ are true
• B. Only $1$ and $5$ are true
• C. Only $1$ and $3$ are true
• D. Only $1$ and $2$ are true
• E. Only $1$ is true

Answer 1

The correct option is E Only $1$ is true

Of the four distributive laws given in statements $\left(1\right),\left(2\right),\left(3\right)$ and $\left(5\right)$ only $\left(1\right)$ holds in the real number field. Statement $\left(4\right)$ is not to be confused with $\log \left(x/y\right)=\log x-\log y.\therefore \left(c\right)$ is the correct choice.